a tripod has three legs each of length 5 feet. when the tripod is set up, the angle between any pair of legs is equal to the angle between any other pair, and the top of the tripod is 4 feet from the ground. in setting up the tripod, the lower 1 foot of one leg breaks off. let $h$ be the height in feet of the top of the tripod from the ground when the broken tripod is set up. then $h$ can be written in the form $\frac{m}{\sqrt{n}}$, where $m$ and $n$ are positive integers and $n$ is not divisible by the square of any prime. find $\lfloor m \sqrt{n} \rfloor$. (the notation $\lfloor x \rfloor$ denotes the greatest integer that is less than or equal to $x$.)

Answers

Answer 1

The value of [m + √n] is 183.

We note that AO=3. From this we can derive that the side length of the equilateral is 3√3. We now use 3D coordinate geometry.A is (0, 0, 0), B is (3√3, 0, 0), C is ((3√3)/2, 9/2, 0), T is ((3√3)/2, 3/2, 4), and S is ((3√3)/10, 3/10, 4/5).We know three points of the SCB plane, so we can write out the equation for the plane. Plane SCB can be expressed as (4√3)x + 4y + 39z - 36 = 0.Applying the distance between a point and a plane formula(ax + by + cz + d)/(√(a² + b² +c²)Put T's coordinates in this in (x, y, z), and replace the values of a, b, c, and d with plane equation coefficients.We get the distance equal to 144/(√1585).A distance of the form m/(√n) is given to us.We have to calculate [m + √n] = [144 + √1585] = 183.

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Related Questions

If you roll a 6-sided die 66 times, what is the best prediction possible for the number of times you will roll an even number?

Answers

Answer:

33 times

Step-by-step explanation:

Set up an equation:

3 evens / 6 total = 1/2 probability of rolling an even

66 times x 1/2 probability= 33

Best prediction: 33 times

Hope this helps!

Determine the constant rate of change

Answers

I think it will be abc definitely

The table shows the current heights and average growth rates of two different species of trees. State and solve an equation to find how long it will take for the two trees to be the same height.

Help with showing equation an answer please!!

Answers

The two different species of plants will take 5 years to reach the same height.

Given, from the table :

Tree specie A has a:

current height = 38 inches

and its annual growth = 4 inches

Therefore, total height is:

38 + 4x .. eq (1)

Tree specie B has a:

current height = 45.5 inches

and its annual growth = 2.5 inches

Therefore, total height is:

45.5 + 2.5x .. eq (2)

Equate equation 1 and equation 2.

38 + 4x = 45.5 + 2.5x

Subtract the constants.

4x = 45.5 - 38 + 2.5x

4x = 7.5 + 2.5x

now subtract the variables.

4x - 2.5x = 7.5

1.5x = 7.5

x = 7.5/1.5

x = 5

Hence the trees will take 5 years to reach the same height.

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How do you add this expression? -1/2 + 2/7

Answers

Answer:

You can't

Step-by-step explanation:



Jasmine spent $2.03 buying party favors for her birthday party. She bought less than ten
identical favors. How much was each one and how many did she buy?
BE SURE YOU ANSWER BOTH QUESTIONS!!
Hint: Each favor costs the same amount

Answers

Given the total spent on buying favors = 2.03 $

Let the number of favors she bought = x

let the amount of each favor = y

She bought favors for less than 10 be

x < 10

The amount she spent can be written as  

x * y = 2.03

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question add 1 1/3 (−5/6) using the number line. select the location on the number line to plot the sum.

Answers

Answer:

Add 11/3+(-5/6)

17/6 it present on number line between

2 and

Step-by-step explanation:

Answer:

1 1/3 (−5/6) using the number line. select the location on the number line to plot the sum

Step-by-step explanation:

What is the factored form of this expression?

Answers

Answer:

The factored form of 27t^3 - 36t^2 - 12t + 16 is:

(3t - 4) (3t+2) (3t - 2)

i have already answered this question but got it wrong but really interested on the right answer

Answers

Answer:

You're right, It's option B.

Step-by-step explanation:

The expressions both share two common factors that are whole numbers; 9 and 6. Use those.

9: 1, 3, 9

6: 1, 2, 3, 6

A company is designing a new cylindrical water bottle. The volume of the bottle will be 179 cm to the power of 3. The height of the water bottle is 8.3 cm. What is the radius of the water​ bottle? Use 3.14 for [tex]\pi[/tex].

Answers

Answer: r=2.62 cm

Step-by-step explanation:

Cylinder Volume: V=πhr^2

179=π(8.3)r^2

179=8.3*3.14*r^2

179=26.062r^2

r^2=6.87

r=2.62 cm

R=2.62cm is going to be your correct answer.

in one city , the ratio of the households with pets to house holds without pets is 30 to 29. if 20,735 households do not have pets, how many house holds have pets

Answers

The number of number of house holds have pets will be 21450 when 20,735 households do not have pets.

What is proportion ?

A proportion is an equation based on the equality of two ratios.

It is given that the ratio of the households with pets to house holds without pets is 30 to 29 and if 20,735 households do not have pets then it is find the number of number of house holds have pets. It can be find out using the ratio correlation :

That is , 29 is the ratio of house holds without pets ⇒ 20735

1 unit of house holds without pet ⇒ 20735/29 = 715 house hold

Now, the ratio of households with pets  ⇒ 30 x 715 = 21450 house hold

Therefore, the number of number of house holds have pets will be 21450 when 20,735 households do not have pets.

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Which graph shows the solution to the system of linear inequalities?

x – 4y < 4

y < x + 1

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.

On a coordinate plane, 2 straight lines are shown. The first dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything above of the line is shaded. The second solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded.

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything above the line is shaded. The second solid line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.

On a coordinate plane, 2 straight lines are shown. The first solid line has a positive slope and goes through (0, negative 1) and (4, 0). Everything below the line is shaded. The second dashed line has a positive slope and goes through (negative 1, 0) and (0, 1). Everything below the line is shaded.

Answers

Answer:

SOLUTION: .−5x + 4y = 20. 10x − 8y = −40.

Step-by-step explanation:

First, solve the first equation for y. Then, substitute for y in the second equation. This equation is an identity

which one of the following pairs of numbers contains like fractions ?
A. 6/7 and 60/79
B.4/8 and 12/16
C. 1/2 and 3/2
D. 5/4 and 4/5

Answers

Answer:

C

Step-by-step explanation:

It’s d. Since it’s the same numbers but switched around. so they are alike

A company sells designer purses For $400 per purse. Usually, they sell 3000 purses per month. according to market research, they will sell 500 more purses for every 20$ reduction in price. write a function R(x) that models the company's revenue, where x is the number of price reductions. find the price that will generate the maximum revenue. find the maximum revenue.

Answers

The price that would yield maximum revenue is $260  and maximum revenue is $1,690,000

What is the revenue function?

The fact that total revenue of  the company is the price per purse multiplied by the number of purses sold, means that the revenue modelled function is simply price multiplied by the quantity sold as shown below:

R(x)=P*x

R(x)=Px

R(3000)=$400*3,000

R(3000)=$1200,000

Note for every 500 more purses, the price reduces by $20

R(3500)=$380*3,500

R(3500)=$1,330,000

R(4000)=$360*4000

R(4000)=$1,440,000

R(4500)=$340*4500

R(4500)=$1,530,000

R(5000)=$320*5000

R(5000)=$1,600,000

R(5500)=$300*5500

R(5500)=$1,650,000

R(6000)=$280*6000

R(6000)=$1680,000

R(6500)=$260*6500

R(6500)=$1,690,000

R(7000)=$240*7000

R(7000)=$1,680,000

The total revenue fell at 7,000 purses, which means that the maximum revenue is $1,690,000 at 6500 purses

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Three fair 6-sided dice are thrown. What is the probability that the three numbers
rolled are three consecutive numbers, in some order?

Answers

The probability that the 3 outcome of numbers obtained are three consecutive numbers is 1/9.

What is defined as the probability?

The probability of an event occurring is calculated by dividing the amount of favourable outcomes by total number of possible outcomes.

Now, as per the given question;

The first number must be either 1, 2, 3, or 4, with a probability;      4/6 = 2/3. The second number must be one higher, which occurs with a probability of 1/6. The third number must then be one greater than the second, which occurs with a probability of 1/6. Therefore the answer to the question about the order;        (2/3)×(1/6)×(1/6) = 2/108.

To address your point, if the three numbers seem to be different, there are 3! = 6 different orders in which they could have been placed.

As a result, the solution to the question;

= (2/3)×(1/6)×(1/6)×6

= (2/3)(1/6)

= 1/9.

Therefore, the probability of getting the three consecutive number is 1/9.

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Point C has coordinates (24, 18).
Point D has coordinates (10, 28).
What are the coordinates of the midpoint of line CD?
Watch video

Answers

Hence , the coordinate of midpoint of line CD is (17 , 23) .

Midpoint refers to some extent that's within the middle of the road connexion 2 points. A centre could be a purpose lying between 2 points and is within the middle of the road connexion the 2 points. If a line is drawn connexion the 2 points, then the centre could be a purpose at the center of the road and is equal from the 2 points.The centre formula is outlined for the points within the coordinate axes. Let (x₁), (y₁) and (x₂), (y₂) be the endpoints of a line section is given by  M = (x₁ + x₂ /2 , y₁ + y₂ /2 ).

We have given two coordinate C (24, 18) and D(10, 28) .

Let M be the midpoint of line CD having coordinate (x,y) .

Using midpoint formula , we get

[tex](x,y) = ( \frac{24+10}{2} ,\frac{18+28}{2} )\\\\(x,y) =( \frac{34}{2} ,\frac{46}{2} )\\\\(x,y) =( 17 ,23 )[/tex]

On comparing , we get coordinate (17 , 23) .

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3 different two-digit numbers are selected and multiplied together. the probability that the product is even is where are relatively prime. what is

Answers

Probability of an even number product as requested = 7/10 = .7 = 70%

The probability is the ratio of the number of outcomes in an exhaustive set of equally likely outcomes that produce a given event to the total number of possible outcomes.

A prime number is a whole number greater than 1 whose only factors are 1 and itself. A factor is a whole number that can be divided evenly into another number. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, and 29.

Combinations of 2 digits from among 5 = 5!/(3!)(2!) = 10. Those combinations of 2 digits resulting in an even number product are even*even and even*odd. There are 2 even digits, (2,4), and 3 odd digits, (1,3,5).

Combinations of 2 even digits and 3 odd digits = 3*2 = 6. Combinations of 2 even digits = 1*1 = 1. there are thus 6+1 = 7 distinct 2 digit products that result in even numbers from among 10 possible 2 digit products.

Probability of an even number product as requested = 7/10 = .7 = 70%

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What is 4 60/72 written as a decimal?

OA) 0.483

OB) 0.83

OC) 4.83

OD) 0.483

Answers

Answer:

C. 4.83

Step-by-step explanation:

60/72 = 0.83333333

so the answer is 4.8333333

25 POINTS AND BRAINLIEST
NO EXPLANATION NEEDED JUST ANSWER

Answers

Answer: 13

Step-by-step explanation:

Write an equation of the line in point-slope form that passes through the
given points. (4, 2) and (1, 6)

Answers

The equation of line that passes through the given points in  point-slope form is y - 2 = -4/3( x - 4 ).

What is the equation of line that passes through the given points?

Given the data in the question;

Point A(4, 2)

x₁ = 4y₁ = 2

Point B(1, 6)

x₂ = 1y₂ = 6

First, we determine the slope of the line.

Slope m = ( y₂ - y₁ )/( x₂ - x₁ )

Slope m = ( 6 - 2 )/( 1 - 4 )

Slope m = ( 4 )/( -3)

Slope m = -4/3

Next, plug the slope -4/3 and point (4,2) into the point slope formula y - y₁ = m( x - x₁ ) and simplify.

y - y₁ = m( x - x₁ )

y - 2 = -4/3( x - 4 )

Therefore, the equation of line that passes through the given points in  point-slope form is y - 2 = -4/3( x - 4 ).

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9. A(n)
is the average of a set of values such that the values hold different levels of importance.

Answers

A mean is the average of set of values such that the values hold different levels of importance.

What is mean?

Mean can be defined as the mathematical average of a group or set of numbers.

It is also the most common value in a collection of numbers.

The formula for determining the mean of a group of data is;

Mean = sum of terms/number of terms

An important and distinct property of the mean is the inclusion of every value in a given set of data of the calculation.

Also, both discrete and continuous data are used in determining the mean.

Thus, a mean is the average of set of values such that the values hold different levels of importance.

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in a small library there are 5 nonfiction books for every 9 fiction book there are 130 nonfiction book

Answers

The number of fiction books in the library are 324, as found by unitary method.

What is unitary method?

A single unit's value can be determined from the values of multiple units, and multiple units' values can be determined from the values of single units using the unitary method.

Given: There are 5 non-fiction books for every 9 fiction books. Total 130 non-fiction books are there in the library.

To find: number of fiction books.

Finding: By unitary method, For every 5 non-fiction books, there are 9 fiction books.

For every 1 non-fiction book, there are 9/5 fiction books.

For every 130 non-fiction books, there are 9/5 × 130 = 324 fiction books.

Hence, The number of fiction books in the library are 324, as found by unitary method.

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(COMPLETE QUESTION:in a small library there are 5 nonfiction books for every 9 fiction book there are 130 nonfiction book. How many fiction books are there in the library?)

PLEASE ANSWER THIS FAST Lesson 16 Practice Problems
1. For each triangle, find the measure of the missing angle.
Figure 3
20°
Figure 1
28
729
128%

K
D
Figure 4
Figure 2 122⁰ 389
7
2. Is there a triangle with two right angles? Explain your reasoning.
56°
89%

Answers

1)

Figure 3: 88°

Figure 4: 35°

Figure 1: 24°

Figure 2: 30°



2)
No, there is not a triangle with two right angles. This is because a right angle is equal to 90°, and two right angles = 180°. Triangles ALWAYS equal 180°, and there are ALWAYS three angles in a triangle. Because of this, it is impossible for a triangle to have two right angles.

Can anyone help me for brainiest 50 points

Answers

Answer: Explanation

Step-by-step explanation:

For #1 first we have to convert all of the fractions to have the same denominator by finding the LCM(Least Common Multiple), which is 60. 1/4=15/60, 1/5=12/60, and 1/3=20/60. Then you add them up and get 47/60. You take that fraction and multiply it by 850 to get about 665.83, which is the estimate.

As for #2, I don't know sorry, I think you can just draw different lengthed lines to show the different distances traveled.

For #3 its 850/9 which is about 94.44

#4 I would recommend stopping through the night because they have about 184 miles to go and since they would only complete about 94 of those miles and would still have to drive tomorrow, they might as well do it all tomorrow.

point M(6.8) was rotated counterclockwise to M'(-8,6). Describe the degrees of the rotation and write an algebraic rule to represent the rotation

Answers

The point is rotated 90° counterclockwise. The algebraic rule for rotation of 90° counterclockwise is (x, y)→(-y, x) .

Rotation of a graph is a transformation where the graph is rotated about a fixed point.

Rotations can happen both clockwise and counterclockwise.To put the graph back in its original position, turn it 360 degrees.The rotated figure's side length is unchanged by rotation.When a polygon is rotated about a fixed point, the modified figure is equal to the original figure.

The given point is M(6,8) . The figure is rotated counterclockwise to get the image M'(-8,6).

Now we have to calculate the degree of rotation of the point.

M(6,8) lies in the first quadrant and M'(-8,6) lies in the second quadrant.

Therefore the rotation is less than 180° .

Now from the figure attached below we can say that the figure was rotated 90°

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Draw a line representing the "rise" and a line representing the "run" of the line. State the slope of the line in simplest form.

Answers

The slope of the line shown is -2/3

Slope of a line

The formula for calculating the slope of a line is expressed according to the formula

Slope = Rise/Run

Slope = y₂-y₁/x₂-x₁

Using the coordinate point (-9,-2) and (-6, -4)

Slope = -4+2/-6+9
Slope = -2/3

Slope = negative two third

Hence the slope of the line shown is -2/3

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Prepare a frequency table of the following scores obtained by 40 students in a
test:
24,16,17,30,28,20,15,24,16,18,18,15,16,20,25,24,25,20,16,15,18,25,20,18,28,27
,25,24,24,18,18,25,20,16,25,20,27,28,28,16.

This contains 20 points please help me quick

Answers

This isn’t with the tally counter since I don’t have paper atm

Score | Frequency
15. 3
16. 6
17. 1
18 6
20. 6
24. 4
25. 6
27. 2
28. 4
30. 1

Answer:

Element  Frequency Cumulative Frequency

15                   3              3

16                   6              9

17                   1              10

18                   6             16

20                   6            22

24                   5            27

25                   6            33

27                   2            35

28                   4            39

30                   1             40

Step-by-step explanation:

Find out how many times an element(data value) appears. That will be the frequency(column 2). The cumulative frequency is the total of all frequencies prior to that element plus the current element frequency

Cumulative frequency for first element is same as its frequency

Cumulative frequency for element 16 is 3 + 6 = 9

Cumulative frequency for element 17 = 3 + 6 + 1 = 9 + 1=10. Basically it is the sum of the previous element cumulative frequency + the current frequency

Members of a soccer team raised $2143.50 to go to a tournament. They rented a bus for $888.50 and budgeted $62.75 per player for meals. Write and solve an equation which can be used to determine xx, the number of players the team can bring to the tournament.

Answers

The equation to find the number of players the team can bring to the tournament is xx = ( 2,143.50 - 888.50 )/62.75 and the number of players the team can bring to the tournament is 20.

An equation is a mathematical statement that shows that two or more mathematical expressions are equal.

Equations express the equality of mathematical expressions by using the equation mark (=).

The total amount raised for the tournament is $2,143.50

The price to rent a bus is $888.50.

The cost of budgeted meals per player is $62.75.

The number of players the team can bring to the tournament is:

xx = ( 2,143.50 - 888.50 ) / 62.75.

xx = ( 2,143.50 - 888.50 ) / 62.75

xx = 1,255 / 62.75

xx = 20

Therefore, the equation to calculate the maximum number of players the team can enter the competition is xx = ( 2,143.50 - 888.50 ) / 62.75.

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Jeremiah makes $15 an hour working part-time at a local fast food restaurant. He pays approximately 11% in taxes on his earnings. If h is his hours worked, model his weekly after-tax wages as a function w(h) of hours worked.

Answers

Step-by-step explanation:

11% = 0.11

the remaining part when subtracting 11% from the whole (100%) is 89%.

89% = 0.89

his after-tax wages are 89% of his total income.

w(h) = 15h × 0.89 = 13.35h

In the figure, =m∠16x° and =m∠2−x8°.

Answers

(a) The equation to find x is :  (6x)°  + (x-8)°  = 90°

(b) The degree measure of the  complementary angles, m∠1 = 84° and m∠2 = 6°

What are complementary angles?

Complementary angles are two angles whose sum is 90 degree.

Given are two complementary angles ∠1 and ∠2 whose measures are given m∠1 = (6x)° and m∠2 =(x-8)°

From the given figure we can see that sum of  ∠1 and ∠2 is 90°, which means they are complementary.

m∠1 + m∠2 = 90°

And  (6x)°  + (x-8)°  = 90°

Or      6x +x-8 = 90

7x = 90+8

7x= 98

x= 98/7 =14

Then m∠1 = (6x)° = (6*14)° = 84° and m∠2 = (x-8)° = (14-8)° = 6°

Therefore, The equation to find x is (6x)°  + (x-8)°  = 90° and measure of the  complementary angles, m∠1 = 84° and m∠2 = 6°

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Determine whether function for the situation would have a discrete or continuous graph.
20. The cost of a given number of handbags
19. Amount of juice in a jug over time.
21. Area of a field based on length 22. Tires in a number of cars.

Answers

The cost of a given number of handbags - Discrete

Amount of juice in a jug over time - Continuous

Area of a field based on length - Continuous

Tires in a number of cars -Discrete

A discrete function as its name suggests has distinct or separate values against one value. That is, one at a time values are in a discrete function. So its domain and image sets will have discrete values.

A continuous function has continuous values within intervals. Its domain will be intervals having a continuous range and images will also be in a  continuous range.

We need to check if the following will have a discrete or a continuous graph:

1. The cost of a given number of handbags.

This is a discrete function as the cost and number of handbags will have discrete values. So it will have a discrete graph.

2. Amount of juice in a jug over time

This is a continuous function. The variables here are the amount of juice and time in which time, clearly, is a continuous variable. So it will have continuous values in an interval. So the amount of juice can also be measured continuously. So the graph will be continuous.

3.  Area of a field based on length

Here the length can take continuous values in an interval. So the area can also be measured continuously giving a continuous graph here.

4. Tires in a number of cars.

Number of tires and number of cars both will take only discrete values. So it can only give a discrete graph.

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What is a printer in SpanishComputadora impresorimpresora campana Which claim does the author's use of false dilemmasupport?-People who live in small towns are strugglingfinancially.-Consumers are going to big-boxstores instead offarmer's markets.-Farmer's markets provide financial support to localbusinesses.-Local support for community businesses is a thing ofthe past. A stack of 9 cups measures 194 mm. Another stack of 22 of the same cups measures 272 mm.1.) Find the height of one cup.2.) How tall would a stack of n cups measure? . which type of bond exemplifies a weak chemical bond? covalent bonds in solution hydrogen bonds in solution ionic bonds in solids nonpolar covalent bonds in solids What is the main difference between japanese capitalism and capitalism in the united states?. an examination into the mental and physical effects of a saffron extract (affron) in recreationally-active adults: a randomized, double-blind, placebo-controlled study Make x the subject of the formulaa=xb^2/2c investigating the influence of experiential training on the ability to anticipate risks of caught-in accidents the price of an airline ticket from denver to chicago costs $450. a bus ticket costs $150. traveling by plane takes 2 hours compared with 32 hours by bus. other things constant, erica would gain by choosing air travel if, and only if, she values her time at more than group of answer choices $5 per hour. $9.38 per hour. $10 per hour. $300 per hour. 13. Which of the following does NOT align with the faith of the Puritans?a.Believed in the tenets of Calvinism, that "the Elect" were pre-destined for salvationby Godb. Believed that Catholicism and the English Church were corrupt, overly ceremonialand hierarchical, and that everyone should read the Biblec.Sought to create a safe haven of religious toleration in their New Englandsettlementsd. Sought to reform the Church of England by setting an example they called the "cityon a hill" all answers needed please help ill give brainliest !! this is due tmr In 2016, American singer-songwriter Bob Dylan was awarded the Nobel Prize in Literature, making him the first musician to ever receive the award. The award sparked debates about whether a musician qualifies for the award. Educate yourself about both sides of the argument and form your own opinion about the topic. Read the four articles provided here to learn more about both sides of the argument.Write an essay to present an argument that either supports or opposes the decision to award a singer-songwriter the Nobel Prize in Literature. Your argument should include a clear claim, logical reasons, and evidence that is relevant and sufficient. Explore the excerpt from "The Tell-Tale Heart" by Edgar Allan Poe to analyze the reliability of the narrator.TRUE!-nervous-very, very dreadfully nervous I had been and am; but why will you saythat I am mad? The disease had sharpened my senses-not destroyed-not dulled them. Aboveall was the sense of hearing acute. I heard all things in the heaven and in the earth. I heardmany things in hell. How, then, am I mad? Hearken! and observe how healthily-how calmly Ican tell you the whole story.It is impossible to say how first the idea entered my brain; but once conceived, it haunted meday and night. Object there was none. Passion there was none. I loved the old man. He hadnever wronged me. He had never given me insult. For his gold I had no desire. I think it washis eye! yes, it was this! He had the eye of a vulture-a pale blue eye, with a film over it.Whenever it fell upon me, my blood ran cold; and so by degrees-very gradually-I made upmy mind to take the life of the old man, and thus rid myself of the eye forever.What sentence shows the reliability of our narrator?(CHOICES IN ATTACHED IMAGE ) today, juan is working in his studio to ensure his prints will remain in place and protected from wrinkling by attaching them to display boards. what is juan most likely doing in preparation for his upcoming exhibit? What is the area of the circle shown below?A circle with radius 8 centimeters.a.8 pi cm2c.StartFraction 16 Over 3 EndFraction pi cm2b.16 pi cm2d.64 pi cm2